Lecture 11 - Chapter 4

1
Lecture 11 - Chapter 4

• Cost Generators
• pages 126-142

2
Overview

• In most networks the single largest expense
  item is the cost of the bandwidth.
• Routers with purchase cost of 10,000(amortized
  cost 300/month) can terminate links that cost
  20,000/month.
• Besides the TRAFFIC table The TARIFF table
  represents the largest data structure needed to
  pose a network problem.

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Types of Tariffs

• Tariff is a published rate for telecommunications
  services and facilities (in U.S. carriers file
  tariffs with FCC).
• 2 types of links
• - usage-insensitive or leased
• - usage-sensitive
• In telephony most individual links are
  usage-sensitive.

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Types of Tariffs Usage Sensitive Voice Tariffs

• A simple usage-sensitive voice tariff
• Fixed cost for the use of line.
• Can place outgoing calls for an additional fee.
• Unlimited incoming calls (the calling party
  pays).
• The tariff is specified in 1-minute increments.

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Types of tariffs Usage-insensitive Voice Tariffs

• Usage-insensitive tariffs come in variety of
  types based on the locations involved.
• Suppose we have a call center located 200 miles
  from a large city, Anagon, where we have several
  hundred customers.

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Types of tariffs Usage insensitive Voice
Tariffs Contd

• Leased line need a tandem voice switch in
  Anagon that can connect the leased line with a
  trunk in the local phone system.
• Out-of-district line gives a line that appears to
  be in Anagon. Reduces the per-minute charge for
  outgoing calls from 0.095 per minute to 0.03
  per minute.
• Banded WATS (wide area telephone service) (4
  hours/day) allows up to 4 hours of calls per
  day to locations that are no more than a certain
  specified distance, for instance 250 miles.

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Types of tariffs Usage-insensitive Voice
Tariffs Contd

• Banded WATS with unlimited usage within the same
  250 mile circle.
• Nationwide WATS - national coverage with
  unlimited usage.
• Banded WATS are more expensive.

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Types of tariffs Usage- sensitive Data
Tariffs

• X.25 and ISDN are deployed in parts of the world.
• Users can place a data call much as they would
  place a voice call .
• Users will be charged a fixed cost a
  cost/minute.
• Optionally users are charged a cost/bit or a
  cost/packet.
• In other parts of the world data on demand is
  limited to modems operating over voice-grade
  lines.

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Types of tariffs Usage-insensitive Data Tariffs

• Limited to speeds consistent with the
  multiplexing hierarchy for the country.
• In U.S. rates are 56 Kbps fractional T1, e.g.
  128 Kbps, 192 Kbps, 256 Kbps, 384 Kbps, 512 Kbps,
  768 Kbps and full T1.
• In Europe there is normally only multiples of 64
  Kbps, including half E1 1024 Kbps.
• Usage-insensitive data tariff for U.K.

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Tariff Taxonomies

• Given the number of ways of buying bandwidth
  and connectivity and the number of ways of paying
  for it, we need a taxonomy of link costs - that
  is to make a decision how to categorize all the
  types of links into a relatively small set of
  examples.
• Note No taxonomy is complete.

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Tariff Taxonomies Link Types Fixed Virtual
Circuits

• Leased links that can be filled with voice calls
  or data at any hour of the day or night.
• They are usually in place for months or years.
• Have substantial installation costs, on order of
  1 or 2 months rent.
• Often derived from higher-speed links by TDM

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Tariff Taxonomies Link Types Dialed
Virtual Circuits

• Can be set up or torn down on demand.
• Often not available at the same speed as fixed
  virtual circuits. Example a T3 link at 45 Mbps
  is only available as a fixed virtual circuit, not
  as dialed virtual circuit.
• Conventional phone uses dialed virtual circuits.

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Tariff Taxonomies Link Types Fixed
Pipes

• Define pipe to be a communication link that
  accepts bits at a certain rate and makes an
  effort (the supplier usually calls it a best
  effort) to deliver the bits to the other end.
  Examples
• Many pipes can share the same physical interface
• Note with virtual circuit the data rate and the
  circuit rate are the same, in pipes they can be
  quite different. Suppose we have frame relay
  connection with 64 Kbps peak rate and a 16 Kbps
  CIR ( committed information rate). We are only
  guaranteed to use the link an average of 0.25 of
  its capacity.

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Tariff Taxonomies Link Types Dialed
Pipes

• Pipes that can be set up or torn down upon
  demand.
• Have the same service characteristics as the
  fixed pipes.
• Charging structure is usage sensitive.

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Tariff Taxonomies Link Types Contd

• Along with the previously described link
  taxonomy we have a list of possible fees
• 1. Access fees ( the cost of maintaining a
  physical network connection).
• 2. Setup fees.
• 3. Teardown fees.
• 4. Usage fees, which depend on
• - channel capacity
• - CIR
• - distance
• - time of day
• - national and administrative borders

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Tariff Taxonomies Relationship to the Network
Design Process

• Q1. How to obtain and organize all the
  information
• mentioned so far in a reasonable way so
  that it
• can be made use of in the design process?
• For Optimization Models we need a simple method
  for obtaining costs.
• Q2. How do we automate the process so that
• gathering the tariff data doesnt become
  the
• largest part of the design process?

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Distance-Based Costing

• Calculating link costs is not very simple.
• Sometimes costs can be very odd.
• The tariff world represents anomalies like those
  found in airline tariffs.
• Example NY-LA cheaper air fares than NY-Montreal
  because of the competition.
• Link from NY- Montreal can be more expensive than
  a link from NY to LA. Competition serves to
  depress the market if there is excess capacity.
  Crossing national borders plays role in
  decreasing competition.

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Linear Distance-Based Costing

• Cost of a circuit between 2 sites that are
  km apart is
• - fixed cost
• - variable cost
• A D64 virtual circuit might have a fixed cost of
  1200 and a variable cost 2.50/km. A circuit of
  200 km will cost 1700/month.
• Unfortunately most tariffs differ significantly
  from this simple model

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Linear Distance-Based Costing Contd

• Interesting use of linear distance-based costing
  is to estimate tariffs when the exact tariff is
  known but is unreasonably complex.
• Tariff may be published as a gigantic table.
  There may be 400 cities in a country, and the
  tariff for a D64 line is published as a table of
  length .
• The table is published on paper. If we do not
  want to scan 100 pages and convert into ASCII via
  OCR (optical character recognition) we can take a
  number of city pairs from the table and fit into
  a linear distance-based tariff.

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Linear Distance-Based Costing Contd

• Represent the data as
  
• where
• Do a least square fit of the data to a linear
  function
• Minimize
  
• Min occurs when the partial derivatives are 0.

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Linear Distance-Based Costing Contd

• Solve in terms of and .
• It will work quite well in certain limited cases
  if all the cites are within a country or within
  the service region of a company within a country,
  the tariff might be exact.
• Example In U.K. we can use the approximation of
• 757.09 2.40/km
• for the cost of a 128 Kbps circuit. In the
  U.S. the circuit between central offices would be
• 605.00 0.49/mile

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Piecewise-Linear Distance- Based Costing

• Definition 4.2. A piecewise-linear function
  on
• with breaks at is
  continuous on and is linear on the
  intervals
  
• Many tariffs are published in piecewise-linear
  format.
• Cost per mile or km is in bands.

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Piecewise-Linear Distance- Based Costing
Contd

• Piecewise-linear tariff for a T1 circuit
  between central offices in the U.S. and Mexico.
• Piecewise linear tariff for 56 Kbps link
  between U.S. and Canada.

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Piecewise-Constant Distance-Based Costing

• Another model for costs is a step function.
• Japanese tariff for a D64 line.

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Tariff Nirvana

• Even if the data is available finding the
  charges can be tricky.
• Q. What would be the ideal solution to the
  tariff problem?
• Tariff library or a tariff client/server
  interface that allowed us to ask for tariffs on
  demand so we could write the following code
• PNODE newyork, paris
• cost tariff_nirvana(newyork, paris,
  T1, ANYCARRIER, FIBER ) and magically
  get the correct result

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Tariff Nirvana Contd

• We are a long way from tariff nirvana
• - often tariffs do not exist
• - while it is easy to get a tariff from
  Dallas to London, it can be another thing to get
  a tariff from Caracas, Venezuela to Beijing,
  China
• - if there are no direct circuits between 2
  countries, there is probably no filed tariff
• - the tariff is not just a function of the 2
  endpoints it also depends on the country where
  the service is booked

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Tariff Nirvana Contd

• Not clear which is the correct tariff to use.
• Good example U.S. and Canada circuits between
  these countries are treated differently from
  other international circuits and differently from
  national circuits.
• Another good tariff example in U.S. with the
  notion of LATA (local access and transport area)
  the cost of a circuit between 2 sites in
  different LATA uses a different tariff than would
  be used if both points are in the same LATA.

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Tariff Nirvana Contd

• Tariffs are misleading could appear that tariff
  offers low rate between 2 sites but when we go
  to provision the circuit we may find that there
  are no facilities or the lead time to provide the
  circuit is unacceptably long.
• There are parts of the world where the cost of a
  simple phone is not prohibitive, but the wait for
  a phone is measured in decades.
• If a network is large enough there are negotiated
  tariffs that allow a carrier to have a special
  deal with a customer.

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Tariff Tools

• Network designers and network operators are the
  single largest group of customers of businesses
  that produce tariff tools and tariff references.
• Companies in the tariff tool business
• - NAC Corp. - PRICER tool produces tariffed
  costs in North America. Extensions of this tool
  cover most of the first world
• - LYNX - LYNXGTD tool is very comprehensive,
  strong on pricing international circuits, weaker
  on prices within countries
• - Tarrifica they produce a tariff book,
  relatively comprehensive

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A Sequence of Cost Generators

• Commercial tariff tools are expensive.
• 5 different cost generators that can generate
  costs for sample problems or for real work are
  described
• Interesting problems can be developed with
  piecewise-linear tariffs.
• Cost Generator 1 and Cost Generator2 for
  academic studies, the other 3 for those who are
  trying to do actual design work.

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Cost Generator 1

• Inputs
• - SITES table with locations in VH or LL
• - TARIFF-UNIVERSAL table as shown below
• Output matrix of size where
  is the number of sites and is the number of
  link types defined in the TARIFF-UNIVERSAL table.

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Cost Generator 1 Contd

• The algorithm passes through all node pairs.
  Fixed cost is abbreviated as and the
  cost/km as
• If distance from to is
  then
• Requires min amount of info to produce cost table
• It will do well within a LATA in U.S. or within a
  country with a simple charging structure like
  U.K.
• Can not produce realistic tariffs covering sites
  in several countries too simple.
• Best way of generating tariffs for test problems
  with min amount of manual work

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Cost Generator 2

• Inputs
• - SITES table with locations in VH or LL
• - TARIFF-UNIVERSAL table as shown below with
  2 additional fields
• Output matrix of size where
  is the number of sites and is the number of
  link types defined in the TARIFF-UNIVERSAL table.

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Cost Generator 2 Contd

• Extends our linear model to a piecewise-linear.
• Not realistic for international tariffs.

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Cost Generator 3

• The costs of services in the U.S. and Mexico are
  quite different as are the costs of services in
  Germany and France. We can deal with it by
  overlaying the output of the Cost Generator 2
  with the country specific information.
• Inputs
• - SITES table with locations in VH or LL
• - TARIFF-UNIVERSAL table as shown below

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Cost Generator 3 Contd

• TARIFF-NAT table as shown below

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Cost Generator 3 Contd

• Output matrix of size where
  is the number of sites and is the number
  of link types defined in the TARIFF-UNIVERSAL
  table.
• is first filled with values from
  the TARIFF-UNIVERSAL table using piecewise-linear
  cost generator. After that is done, a second pass
  through the sites is taken. If the country code
  for site and are both country ,
  then we recalculate the tariff for the node pair
  

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Summary

• Traffic and cost generation allows us to take the
  SITES table of entries and produce the
  TRAFFIC and TARIFF tables which have
  entries.
• If these tables were produced manually they would
  take up most of our time which could be used to
  create good designs.
• Traffic and cost generators are packaged into a
  single program called network generator which
  allows us to pose a complete design problem.